In this paper, an inversion algorithm for the retrieval of ozone and other constituent profiles in the Earth's lower atmosphere from spectroscopic stellar occultation measurements is developed and evaluated through simulated retrievals. In addition to extinction by absorption and scattering, the effects of refractive bending, refractive attenuation, scintillation, and spatial variations in the extinction cross sections along the line of sight introduced by temperature dependence in absorption cross sections or variations in aerosol properties are considered. For computational efficiency, the inversion is conducted in two stages. The transmission spectra are first fitted to obtain the line-of-sight column quantities, followed by a spatial inversion to retrieve the vertical profiles. The use of smoothness constraints and a priori information are investigated. Retrieval simulations conducted for reasonable instrument parameters and measurement noise (described within) demonstrate that ozone profiles can be retrieved between 15 and 50 km with statistical uncertainties better than 5% (2% at the ozone peak) and systematic bias better than 0.5%. Although these accuracies depend upon the particular measurement scenario (i.e., stellar type and magnitude, instrument noise, etc.), they are representative of the results expected for a properly optimized stellar occultation experiment.